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The boolean expression $\left(\right(p\wedge q)\vee (p\vee \sim q\left)\right)\wedge (\sim p\wedge \sim \text{q})$ is equivalent to:

A cone has its radius(R) equal to its height. What is the volume of its frustum if the smaller cone’s radius is 'r' ?

If $2x^2{y}^2+y^2-6x^2-12=0,$ then number of integral pairs $(x,y)$ satisfying is/are

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0); focus (3, 0)

An analytic function of a complex variable $z=x+iy$ is expressed as $f\left(z\right)=u(z,y)+iv(x,y),$ where $i=\sqrt{-1}$. if $u(x,y)=x^2,$ then expansion for $v(z,y)$ in terms of $x,y$ and a general constant $c$ would be

Total number of six-digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is

The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is

If the dc's of two lines parallel lines are given by $2l+3m+kn=0$ and $l^2-m^2+5n^2=0$ then the values of k are:

How many different (mutually noncongruent) trapeziums can be constructed using four distinct side lengths from the set $\{1,3,4,5,6\}?$

Let $xtan\alpha +ysin\alpha =\alpha ,\alpha xcosec\alpha +ycos\alpha =1$ be two straight lines. Let P be the point of intersection of the lines in the limiting position when \alpha \rightarrow 0, if the point P is (h, k), then |h + k| is___.

There are three copies each of four different books. The number of ways in which they can be arranged in a shelf is

${\left[\right(B^{\prime }\cup (B^{\prime }-A)\left)\right]}^{\prime }$ =___

If $f\left(x\right)=\underset{0}{\overset{x}{\int }}{e}^t\sin (x-t)dt,$ then $f^{\prime \prime }x-f\left(x\right)$ is equal to

Find $\frac{dy}{dx}$ if y is a function of x and $(x+y{)}^2=x-y+1$.

Find the equation of the straight lines passing through the origin and making an angle of ${45}^{\circ }$ with the straight line $\sqrt{3}x+y=11$

The positive value of $\lambda$ for which the co-efficient of $x^2$ in the expression $x^2{(\sqrt{x}+\frac{\lambda }{x^2})}^{10}$ is $720$, is :

Number of ways of arranging $5$ different objects in the squares of given figure in such a way that no row remains empty and one square can't have more then one object.

If the equation of the parabola whose focus is the point of intersection of $x+y=3,$ $x-y=1$ and directrix is $x-y+5=0,$ is $a{x}^2+bxy+c{y}^2+dx+ey-15=0,$ then the radius of the circle $a{x}^2+c{y}^2+dx+ey-10=0$ is equal to

A die
marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the
event, ‘the number is even,’ and B be the event, ‘the
number is red’. Are A and B independent?

The length of the latus rectum of the parabola $25\left[\right(x-2{)}^2+(y-4{)}^2]=(4x-3y+12{)}^2$ is

Let $t_1,t_2,t_3$ be three points on the parabola $y^2=4x$. If the normal at $t_1$ intersects the parabola at $t_2$ and the normal at $t_2$ intersects the parabola at $t_3$ such that $3t_1+13t_2+9t_3=0$, then

Find the principal values of the following questions:

$cosc{e}^{-1}(-\sqrt{2})$

Write the middle term in the expansion of ${(x+\frac{1}{x})}^{10}.$

Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

If $n$ is an odd integer, $i=\sqrt{-1}$, then $(1+i{)}^{6n}+(1-i{)}^{6n}$ is equal to

The sides of a triangle are $sin\alpha ,cos\alpha$ and $\sqrt{1+sin\alpha cos\alpha }$ for some $0<\alpha <\frac{\pi }{2}$. Then, the greatest angle of the triangle is

The system of linear equations $x+y=0,x–y=0,z=0$ will have

The keys 12, 18, 13, 2, 3, 23, 5 and 15 are inserted into an initially empty hash table of length 10 using open addressing with hash function h(k) = k mod 10 and linear probing.

What is the resultant hash table?

The number of integers a in the interval [1,2014] for which the system of equations $x+y=a;\frac{x^2}{x-1}+\frac{y^2}{y-1}=4$ has finitely many solutions is

Let a > 0 be a real number. Then the limit $\underset{x\to 2}{lim}\frac{a^x+a^{3-x}-(a^2+a)}{a^{3-x}-a^{\frac{x}{2}}}$ is